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Distributed MPC with ALADIN – A Tutorial [article]

Boris Houska, Jiahe Shi
2022 arXiv   pre-print
The focus is - for simplicity of presentation - on convex quadratic programming (QP) formulations of MPC.  ...  , as well as barrier or interior point methods.  ...  In this example, the ALADIN based algorithm with log-barrier updates detects the optimal active set during iteration 729. for all x, x ′ in the feasible domain of J ∞ .  ... 
arXiv:2204.01654v1 fatcat:zjlzx5l54re3nkk424c5qnk75e

Page 718 of Mathematical Reviews Vol. , Issue 97A [page]

1997 Mathematical Reviews  
This paper presents a method for the line-search procedure used in barrier function methods for solving convex quadratic progam- ming problems with quadratic constraints.  ...  Generalized convex relations with applications to optimization and models of economic dynamics. (English summary) Set-Valued Anal. 4 (1996), no. 1, 67-89.  ... 

Recent Developments in Interior-Point Methods [chapter]

Stephen J. Wright
2000 IFIP Advances in Information and Communication Technology  
In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semidefinite  ...  The modern era of interior-point methods dates to 1984, when Karmarkar proposed his algorithm for linear programming.  ...  Powell and the other organizers of the IFIP TC7 '99 conference for arranging a most enjoyable and interesting meeting, and for a dose reading of the paper which resulted in many improvements.  ... 
doi:10.1007/978-0-387-35514-6_14 fatcat:chzlfupe7bbhbdyynhatlckjcu

Page 9751 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
The first 2003m:90088 is of the active-set variety.  ...  and S CR" is a convex and closed set.  ... 

A Log-Barrier Method for Mesh Quality Improvement [chapter]

Shankar P. Sastry, Suzanne M. Shontz, Stephen A. Vavasis
2011 Proceedings of the 20th International Meshing Roundtable  
The technique can be used with convex or nonconvex quality metrics. The method uses a logarithmic barrier function and performs global mesh quality improvement.  ...  Our method usually yields better quality meshes than existing methods for improvement of the worst quality elements, such as the active set, pattern search, and multidirectional search mesh quality improvement  ...  The work of the third author was supported in part by a Discovery grant from NSERC (Canada) and a grant from the U.S. Air Force Office of Scientific Research.  ... 
doi:10.1007/978-3-642-24734-7_18 dblp:conf/imr/SastrySV11 fatcat:r4befxl27bd43n34of6snqkgz4

Page 5356 of Mathematical Reviews Vol. , Issue 2002G [page]

2002 Mathematical Reviews  
For feasible point procedures or active set strategies such infor- mation is essential to shrinking down the problem size and to speeding up iterations.  ...  (D-DORT-OR; Dortmund) Identifying non-active restrictions in convex quadratic programming.  ... 

PPD-IPM: Outer primal, inner primal-dual interior-point method for nonlinear programming [article]

Martin Neuenhofen
2018 arXiv   pre-print
So far all algorithms for NLP are based on either of the following three principles: successive quadratic programming (SQP), active sets (AS), or interior-point methods (IPM).  ...  These are in order: iteration complexity, feasibility management in the sub-program, and utility of initial guesses. Our novel approach attempts to overcome these drawbacks.  ...  The problem however with ASM is that there is no polynomially efficient method for determining the optimal active set A.  ... 
arXiv:1803.01829v1 fatcat:khw2ryagzjh53ih3e2allo5s6e

Constructing Self-concordant Barriers for Convex Cones

Yurii Nesterov
2006 Social Science Research Network  
Thus, our abilities in constructing good barriers for convex sets and cones become now identical.  ...  We start from a simple proof for a variant of standard result [1] on transformation of a ν-self-concordant barrier for a set into a self-concordant barrier for its conic hull with parameter (3.08 √ ν +  ...  The general barrier calculus was developed in [8] only for convex sets.  ... 
doi:10.2139/ssrn.921790 fatcat:rkbfsz344ffedouycygfyzpkj4

Interior-point methods

Florian A. Potra, Stephen J. Wright
2000 Journal of Computational and Applied Mathematics  
, and convex programming over sets that can be characterized by self-concordant barrier functions.  ...  In the years since then, algorithms and software for linear programming have become quite sophisticated, while extensions to more general classes of problems, such as convex quadratic programming, semi-deÿnite  ...  Given a ÿnite-dimensional real vector space V, an open, nonempty convex set S ⊂ V, and a closed convex set T ⊂ V with nonempty interior, we have the following formal deÿnition. Deÿnition 1.  ... 
doi:10.1016/s0377-0427(00)00433-7 fatcat:kwhchrvwcncsvmkd7cdjy3wpny

Primal-dual interior-point methods [chapter]

2010 Polyhedral and Semidefinite Programming Methods in Combinatorial Optimization  
, and convex programming over sets that can be characterized by self-concordant barrier functions.  ...  W e review some of the key developments in the area, including comments on both the complexity theory and practical algorithms for linear programming, semide nite programming, monotone linear complementarity  ...  Given a nite-dimensional real vector space V, an open, nonempty convex set S V , and a closed convex set T V with nonempty i n terior, we h a ve the following formal de nition.  ... 
doi:10.1090/fim/027/04 fatcat:ps2izalopfhetgouzqqjcy7oti

Convergent filtered scheme for the Monge-Ampère Equation [article]

Ricardo H. Nochetto, Dimitrios Ntogkas
2018 arXiv   pre-print
The method combines our original monotone operator with a more accurate non-monotone modification, using an appropriately chosen filter.  ...  This results in a remarkable improvement of accuracy, but without sacrificing the convergence to the unique viscosity solution.  ...  Walker for providing assistance and guidance with the software FELICITY and to H. Antil for numerous discussions about the implementation of the method. We also thank W.  ... 
arXiv:1807.04866v1 fatcat:auoosru3nnboblxm6l3jxot7b4

Page 1877 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
Summary: “We study active set methods for optimization prob- lems in block angular form (BAF).  ...  Summary: “A convex-valued, upper continuous multifunction with pointed closed convex domain is proved to be onto, if there is a selection with certain coercive properties and if the selection for each  ... 

Soil creep and convex-upward velocity profiles: theoretical and experimental investigation of disturbance-driven sediment transport on hillslopes

Joshua J. Roering
2004 Earth Surface Processes and Landforms  
The height of neighbouring particles (which is akin to activation energy in chemical reactions) varies with slope angle such that energy barriers get smaller in the downslope direction as slopes steepen  ...  Using tracer particles, we observed a convex-upward velocity profile near the surface of the sandpile, consistent with predictions of our RPT-based velocity model.  ...  Sklar aided in the construction of the experimental apparatus and E. Montanaro performed numerous experimental analyses with care and patience.  ... 
doi:10.1002/esp.1112 fatcat:pkfnbtuq4vel5blzadltqhoz2a

Page 7800 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
An empirical study shows that this value, when used with a larger scaling factor in linear scaling, improves the performance of the genetic algorithm.  ...  of all active constraints at a point of degeneracy, thus making them attractive in combinatorial settings where the linear program is represented implicitly.”  ... 

Numerical methods for large-scale nonlinear optimization

Nick Gould, Dominique Orban, Philippe Toint
2005 Acta Numerica  
State-of-the-art algorithms for solving unconstrained, bound-constrained, linearly-constrained and nonlinearly-constrained problems are discussed.  ...  The authors are indebted to Annick Sartenaer for her comments on a draft of the manuscript. Numerical methods for large-scale nonlinear optimization  ...  The work of the third author has been conducted in the framework of the Interuniversity Attraction Poles Programme of the Belgian Science Policy Agency.  ... 
doi:10.1017/s0962492904000248 fatcat:dz3twiovzfekxawl2h3wfi3m44
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